{
  "id": "1412.8567",
  "version": "v1",
  "published": "2014-12-30T06:13:19.000Z",
  "updated": "2014-12-30T06:13:19.000Z",
  "title": "On sums of fourier coefficients of automorphic forms for $gl_r$",
  "authors": [
    "Jaban Meher"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For $r\\ge 2$, let $\\pi$ be an irreducible cuspidal automorphic representation of $GL_r(\\mathbb{A}_{\\mathbb{Q}})$ with unitary central character. Let $a_\\pi(n)$ be the $n^{th}$ coefficients of the $L$-function attached to $\\pi$. Goldfeld and Sengupta have recently obtained a bound for $\\sum_{n\\le x} a_\\pi(n)$ as $x \\rightarrow \\infty$. For $r\\ge 3$ and $\\pi$ not a symmetric power of $GL_r(\\mathbb{A}_{\\mathbb{Q}})$ cuspidal automorphic representation, their bound is better than all previous bounds. The goal of this paper is to further improve the bound of Goldfeld and Sengupta.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-30T06:13:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphic forms",
      "fourier coefficients",
      "irreducible cuspidal automorphic representation",
      "unitary central character",
      "symmetric power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}